Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866908454998769664 |
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| author | Chen, Youming |
| author_facet | Chen, Youming |
| contents | The purpose of this paper is to study the properties of holomorphic Poisson manifolds $(M,π)$ under the assumption of $\partial_{}\bar{\partial}$--lemma or $\partial_π\bar{\partial}$--lemma. Under these assumptions,we show that the Koszul--Brylinski homology can be recovered by the Dolbeault cohomology, and prove that the DGLA $(A_M^{\bullet,\bullet},\bar{\partial},[-,-]_{\partial_π})$ is formal.Furthermore,we discuss the Maurer--Cartan elements of $(A_M^{\bullet,\bullet}[[t]],\bar{\partial},[-,-]_{\partial_π})$ which induce the deformations of complex structure of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_14511 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds Chen, Youming Differential Geometry The purpose of this paper is to study the properties of holomorphic Poisson manifolds $(M,π)$ under the assumption of $\partial_{}\bar{\partial}$--lemma or $\partial_π\bar{\partial}$--lemma. Under these assumptions,we show that the Koszul--Brylinski homology can be recovered by the Dolbeault cohomology, and prove that the DGLA $(A_M^{\bullet,\bullet},\bar{\partial},[-,-]_{\partial_π})$ is formal.Furthermore,we discuss the Maurer--Cartan elements of $(A_M^{\bullet,\bullet}[[t]],\bar{\partial},[-,-]_{\partial_π})$ which induce the deformations of complex structure of $M$. |
| title | Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2209.14511 |